Session 11

Elastic Mechanics

The basic model for an elastic body (membrane) reads

  • dv/dt – dsx/dx – dsy/dy =0
  • dsx/dt = dv/dx, dsy = dv/dy,

where v is (transversal) displacement velocity and sx and sy stresses in x and y-direction. Shorthand: dv/dt = div s, ds/dt = grad v.

Introduction of displacement u by du/dt = v gives the model in terms of displacement (instead of velocity)

  • dv/dt – dsx/dx – dsy/dy = 0,
  • du/dt = v, sx = du/dx, sy = du/dy

or

  • dv/dt – Δu = 0, du/dt = v.